Which of the following octahedral complexes is expected to have the largest crystal field splitting ${\Delta }_o$?

With the same ligand, ${\Delta }_o$ rises with metal oxidation state (3+ over 2+) and moves down a group (3d < 4d < 5d) because larger, more diffuse d orbitals overlap more with ligands. Ir(III) is a 5d ion of charge 3+, so $[\mathrm{Ir}(\mathrm{NH}{}_3){}_6]{}^{3+}$ has the largest ${\Delta }_o$.